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Search: id:A068772
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| A068772 |
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Generalized Catalan numbers. |
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+0
3
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| 1, 1, 20, 410, 8600, 184200, 4020000, 89205000, 2008700000, 45816140000, 1056825200000, 24618524200000, 578457724000000, 13695679012000000, 326448619920000000, 7827776361090000000, 188701194087000000000
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OFFSET
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0,3
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COMMENT
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This is the tenth member in the a-family of sequences K(a,a; n), a=1,2,3,...,n>=0, defined in a comment to the array A068763.
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FORMULA
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a(n)=(10^n)*p(n, -9/10) with the row polynomials p(n, x) defined from array A068763.
a(n+1)= 10*sum(a(k)*a(n-k), k=0..n), n>=1, a(0)=1=a(1).
G.f.: (1-sqrt(1-40*x*(1-9*x)))/(20*x).
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CROSSREFS
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Cf. A000108, A068764-71, A025227-30.
Sequence in context: A055476 A041181 A041762 this_sequence A158601 A130832 A109116
Adjacent sequences: A068769 A068770 A068771 this_sequence A068773 A068774 A068775
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Mar 04, 2002
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